This paper presents a robust predictive control scheme with a graphic-based delay boundary analysis to mitigate the electric vehicle (EV) drivetrain oscillating issues, subject to the multi-channel compounding-construction loop delays. The application of Controller Area Network (CAN) in autonomous electric vehicles (AEVs) inevitably induces multi-channel compounding-construction loop delays into the control loop. The in-deep analyzing and understanding of the network-induced loop delays is critical for the electrified powertrain and its motion control. This study aims to guarantee, explicitly, the motion stability of AEV drivetrains as safe-critical and hard real-time applications. Firstly, a graphic-based constructional representation approach is presented for modeling of the compounding-construction loop delays. To resolve the upper bound of the compounding-construction loop delays further, a mathematic expression of delay boundary-envelopment analysis is derived. Secondly, based on the reasonable upper bound, Taylor series expansion is applied to make the system model with nonlinear uncertainties caused by the network-induced loop delays represent in the form of the convex polytope. Then, with the convex polytope of the drivetrain system model, a robust model predictive control (RMPC) approach is developed to enhance the system robustness against the unexpected network-induced delays. To attenuate the online calculation burden, a scheme combining off-line design and on-line synthesis is provided. Finally, the satisfactory motion control performance in both the co-simulations (Matlab&Carsim) and bench experimental tests can strongly verify the effectiveness of the proposed approaches.